{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IZA7SIADSJ2LPFFQM6PS2E7HEO","short_pith_number":"pith:IZA7SIAD","canonical_record":{"source":{"id":"1408.0127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-01T10:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"df905c87f42f329e262c9a724702bd8fa44bb83624b591142f2fa162a4f8a113","abstract_canon_sha256":"02289f35ad9b3eea81326aa3c2df4a6c492859bfa81ab15f4633f1185b176ed3"},"schema_version":"1.0"},"canonical_sha256":"4641f920039274b794b0679f2d13e723b27e25b7a811cff7b977b1528cbb171b","source":{"kind":"arxiv","id":"1408.0127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0127","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0127v1","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0127","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"IZA7SIADSJ2L","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IZA7SIADSJ2LPFFQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IZA7SIAD","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IZA7SIADSJ2LPFFQM6PS2E7HEO","target":"record","payload":{"canonical_record":{"source":{"id":"1408.0127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-01T10:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"df905c87f42f329e262c9a724702bd8fa44bb83624b591142f2fa162a4f8a113","abstract_canon_sha256":"02289f35ad9b3eea81326aa3c2df4a6c492859bfa81ab15f4633f1185b176ed3"},"schema_version":"1.0"},"canonical_sha256":"4641f920039274b794b0679f2d13e723b27e25b7a811cff7b977b1528cbb171b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:03.814471Z","signature_b64":"UNBhfeEDv7l56VjgCpf3NlJ+V9CEsdVoR3jMmBfOdaQ45T30oJpJB7bvrOVJpb4vK8uqdsYfAYZo5KN2K3RiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4641f920039274b794b0679f2d13e723b27e25b7a811cff7b977b1528cbb171b","last_reissued_at":"2026-05-18T02:46:03.813952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:03.813952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.0127","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+aliJ0e6/AQkrdYuacD8K+FAyoVWolto3UHVHuO92cIjtx0Y7YbxdPp/7wKquwSaItSpfF9sThL87I6xM7QxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:16:47.456091Z"},"content_sha256":"c3a7c0b4c55d016e983f1e6370014c77d45c3b837b9a7b63ee439ee91f76e8a1","schema_version":"1.0","event_id":"sha256:c3a7c0b4c55d016e983f1e6370014c77d45c3b837b9a7b63ee439ee91f76e8a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IZA7SIADSJ2LPFFQM6PS2E7HEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Using Hoare's Theorem to find the signature of a subgroup of an NEC group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"David Singerman","submitted_at":"2014-08-01T10:53:25Z","abstract_excerpt":"We explain how to use Hoare's Theorem to find the signature of a subgroup of an NEC group. We give several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0127","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxfaTpqsyFNhQwgFi3oPa3UJLFzPdlCzTasxJftWp34ojMN5pDzX3+Cbdy9WWlA/9dlpPCbeqrAiwhm3grBRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:16:47.456433Z"},"content_sha256":"948d5304dbc485c75563be4fcc265a188ce24f4d2f9fb0926f57d275473c4682","schema_version":"1.0","event_id":"sha256:948d5304dbc485c75563be4fcc265a188ce24f4d2f9fb0926f57d275473c4682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/bundle.json","state_url":"https://pith.science/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T11:16:47Z","links":{"resolver":"https://pith.science/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO","bundle":"https://pith.science/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/bundle.json","state":"https://pith.science/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZA7SIADSJ2LPFFQM6PS2E7HEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IZA7SIADSJ2LPFFQM6PS2E7HEO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"02289f35ad9b3eea81326aa3c2df4a6c492859bfa81ab15f4633f1185b176ed3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-01T10:53:25Z","title_canon_sha256":"df905c87f42f329e262c9a724702bd8fa44bb83624b591142f2fa162a4f8a113"},"schema_version":"1.0","source":{"id":"1408.0127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0127","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0127v1","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0127","created_at":"2026-05-18T02:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"IZA7SIADSJ2L","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IZA7SIADSJ2LPFFQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IZA7SIAD","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:948d5304dbc485c75563be4fcc265a188ce24f4d2f9fb0926f57d275473c4682","target":"graph","created_at":"2026-05-18T02:46:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We explain how to use Hoare's Theorem to find the signature of a subgroup of an NEC group. We give several examples.","authors_text":"David Singerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-01T10:53:25Z","title":"Using Hoare's Theorem to find the signature of a subgroup of an NEC group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0127","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c3a7c0b4c55d016e983f1e6370014c77d45c3b837b9a7b63ee439ee91f76e8a1","target":"record","created_at":"2026-05-18T02:46:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"02289f35ad9b3eea81326aa3c2df4a6c492859bfa81ab15f4633f1185b176ed3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-01T10:53:25Z","title_canon_sha256":"df905c87f42f329e262c9a724702bd8fa44bb83624b591142f2fa162a4f8a113"},"schema_version":"1.0","source":{"id":"1408.0127","kind":"arxiv","version":1}},"canonical_sha256":"4641f920039274b794b0679f2d13e723b27e25b7a811cff7b977b1528cbb171b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4641f920039274b794b0679f2d13e723b27e25b7a811cff7b977b1528cbb171b","first_computed_at":"2026-05-18T02:46:03.813952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:03.813952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UNBhfeEDv7l56VjgCpf3NlJ+V9CEsdVoR3jMmBfOdaQ45T30oJpJB7bvrOVJpb4vK8uqdsYfAYZo5KN2K3RiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:03.814471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3a7c0b4c55d016e983f1e6370014c77d45c3b837b9a7b63ee439ee91f76e8a1","sha256:948d5304dbc485c75563be4fcc265a188ce24f4d2f9fb0926f57d275473c4682"],"state_sha256":"92dd1071a086dc4d7ea2830a8f1729f26d77fbe08697f306155e0456df9101fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUJijHYpRqC8vkXGgKCOeCO+lQBq87jhBTbxYbKuYN5CKziAYItLmrCEbsBKokJvZIE8FCIhsVs+ZoTfECylDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:16:47.458241Z","bundle_sha256":"19e0f6bcf1dc9f689b026b1f2313807bc73a2bf930d35f85f191c9db9afa7438"}}